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A glass tube int the form of an equilate...

A glass tube int the form of an equilateral triangle of uniform cross-section is as shown in figure. It lies in the vertical plane, with base horizontal . The tube is filled with equal volumes of three immiscible liquid whose densities are in arithmetic progession. Determine the length x as shown in figure

A

3 l

B

2 l

C

l/3

D

l/2

Text Solution

Verified by Experts

The correct Answer is:
C
Pressure ,at A,
Due to left arm, `P=dg(l-x)sin60^(@)+(d+2y)gx sin 60^(@)`
Due to right arm, `P=dgx sin60^(@) + (d+y)g(1-x)sin60^(@)`
Equation the two values of pressure for equilibrium,
`dg(l-x)(sqrt(3))/(2)+(xsqrt(3))/(2)(d+2y)g=(xsqrt(3))/(2)dg+(l-x)(sqrt(3))/(2)(d+y)g`
or `(l-x)d+x(d+2y)=xd+(l-x)(d+y)`
or `ld-xd+xd+2xy=xd+ld-xd-xy`
`implies 2yx=y(l-x)` or `2x=l-x`
`therefore x=(l)/(3)`
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